The action takes place in Gaul during the Roman occupation, around 50 BC.
The sacred grove of the druids. The warriors and druids of the tribe of the Sicambri have gathered to wait for the rising of the new moon, when Norma, the high priestess, will perform religious ceremonies and consult the will of the god Irminsul. Inspired by the chief druid, Oroveso, father of Norma, the people express the hope that the god will favor their projected uprising against the hated Romans. The Gauls go off into the forest and Pollione, the Roman proconsul, and his friend, the centurion Flavio, enter cautiously. Pollione confides that he no longer loves Norma who, although supposed to be a virgin priestess, has secretly borne him two sons. He is now in love with a temple virgin, Adalgisa, and fears Norma’s vengeance when she learns of his perfidy. As the Gauls can be heard returning, the Romans leave, as it is death for them to be found there. The Gauls reassemble and Norma appears, reproaching them for expressing warlike sentiments in the sacred grove and before the will of the god has been ascertained. She tells them that the time is not yet ripe for rebellion, but prophesies the eventual fall of Rome. She cuts the sacred mistletoe, invokes the moon and prays for peace. The druids and warriors continue to press for war, with the death of Pollione as the first blow. Norma promises them that he will fall, but expresses to herself the hope that he will return to her with all the ardor of his first love, which she has felt to be waning. Everyone leaves the grove except Adalgisa. Pollione returns and tells her of his love. Revealing that he has to leave for Rome the next day, he begs her to fly with him. Although she returns his love, she is unwilling to break her vows, but eventually allows herself to be persuaded.
Norma’s secret dwelling in the forest. Norma is distressed by the presence of her two sons, who remind her of Pollione, and she tells her attendant Clotilde to take them away and hide them safely. Adalgisa approaches nervously to confess that she is tormented by a love which is stronger than her vows. As she relates the coures of her love, without naming its object, Norma grows more sympathetic, remembering her own similar experiences.
She releases Adalgisa from her vows and asks who she loves. To her horror Adalgisa points to Pollione, standing outside. He rushes in, too late to prevent her revelation, and is confronted by Norma, who accuses him of treachery to her and deceit towards Adalgisa, whom she does not blame, but pities. Pollione prepares to leave and calls on Adalgisa to join him. Overcome with horror at his perfidy, she spurns him, while Norma threatens him with vengeance. The sacred gong is struck, summoning Norma to the altar, and she tells Pollione that it portends his death.
Inside Norma’s dwelling. Norma hovers over her sleeping children with a knife, intending to kill them and then herself, fearing their fate if they are left unprotected. But, even to be avenged on Pollione, she is unable to kill them and tells Clotilde to summon Adalgisa. Still resolved to die, she tells Adalgisa to marry Pollione and entrusts the children to her, begging her to take them to Rome and protect them. Adalgisa protests that she has no further thoughts of marrying Pollione or leaving her country and begs Norma, in the name of her children, to sapre herself. She promises to plead with Pollione to return to Norma, expressing her confidence that he has already repented of his disloyalty, and Norma is persuaded.
The druids’ temple. The Gauls, although still plotting rebellion, are prepared to dissemble for a while longer if necessary. Norma’s hopes that Pollione will return to her are shattered by Clotilde, who tells her that he still plans to take Adalgisa away with him. Impelled by her wish for vengeance, Norma strikes the sacred gong to summon the tribe, and tells them that the time is now ripe for rebellion, urging them to sound their war-cry. Oroveso asks her to complete the necessary sacrificial rites. Pollione is dragged in, having been caught trying to carry off Adalgisa by force. Norma sends the tribe away, saying she must interrogate Pollione privately. She exults that he is now in her hands, but promises to free him if he will swear to forget Adalgisa. She is so enraged by his refusal that she threatens to punish Adalgisa too, and is triumphant when he is reduced to pleading -not for himself, but for Adalgisa. Norma calls the druids and warriors back, promising Pollione that she will punish him through Adalgisa. She announces that she has discovered that one of the priestesses has broken her vows and betrayed her country. When the tribe demands to know the name of the offender, Norma finds herself unable to name the innocent Adalgisa, and names herself, bidding Pollione see what a noble soul he has spurned. He is overcome by remorse at last, declaring that his love for her has returned and he will gladly die with her. Preparing to ascend the pyre which is being constructed for their execution, Norma confesses the existence of her sons and begs her father Oroveso to protect them. His resistance is overcome by her pleading and Norma and Pollione ascend the pyre together.